Although \(T_0[n] + E_{xc}[n]\)  is universal,[1]} there exists no
simple means thus far to obtain it. As a consequence, various ad hoc exchange-correlation density functionals
have been suggested/needed to yield acceptable results in different settings [2]}, [3]}, [4]}, [5]}
when employing the Kohn-Sham scheme.
Limitations of these approximate functionals have been discussed.[6]}, [7]}
Some of the failures while using ad hoc density functionals can be attributed to
misuse of the density-functional theory. For example,
it is sometimes neglected that the electron density \(n({\bf x})\)  achievable
via introduction of a source potential
must obey \(\int n({\bf x}) d{\bf x}= N_e\)  and
does not cover the functional space \(\lbrace  n({\bf x}) \ge 0 \rbrace \) , a problem also known
as the \(\upsilon \) -representability. [8]}, [9]}, [10]}
As pointed out in reference VF95,
neglecting these constraints may lead to conclusions [11]} that are
not always valid.
